[Math] Justify, without evaluating, that the determinant of the following matrix is zero

Question

I am currently stuck at this question and have no idea how to solve.
I just started out learning linear and I'm really weak in this field.

Justify, without evaluating, that the determinant of the following matrix is zero

Here's the matrix A:

$$\begin{pmatrix}
1 & 0 & 2 & 4\\
-2 & 3 & 8 & 6\\
-1 & 3 & 10 & 10\\
6 & 6 & -3 & 7\\
\end{pmatrix}$$

I searched online but couldn't find something similar.
What I found though was that if it was skew-symmetric ($A^t= -A$)
then the determinant could directly be said to be equal to zero.
But in this case it didn't work with me.

Thank you.

Answer 1

The third row is the sum of the first and second rows. The rows are not linearly independent, so the determinant is zero.